When considering unbalance in a keyed shaft application, how does everybody calculate what length key stock they need to install to keep things in balance? We have run into some apparent problems in the past with unbalance, and we traced it back to improper length key. We have a lot of high speed fans, that are all belted "speed up" configurations. All of our fan shafts are custom made, with key slots that vary in length. For instance, on a 3" shaft, some key slots are 4" in length while other shafts of the same size have a key slot 7" in length (don't ask why). So how does one go about calculating the proper length key for any given application?

In our situation, here's what happened. We switched speeds of some of our fans, and that required a smaller driven sheave, that in turn required a different taper lock bushing, which in turn used a 3/4 height (rectangular) key as compared to the full (square) key that we had been using. Conveniently enough, the new bushings came with a 3/4 key that was the exact length of the bushing. So the mechanics, without questioning, installed the new sheaves and bushings with the provided key. This left about 4-1/2" of unused key slot in the shaft (a void about 1/2" x 3/4" x 4-1/2"). These fan shafts turn 2350 RPM. Now all hell breaks loose because things are very much out of balance.

When we first discovered we had this problem, we decided to base our calculation for a proper length key on a "one for one" total volume of the key slots vs. key stock. In other words, if we had a square (full) key, and the shaft had a 4" slot and the corresponding bushing had a 2" slot, we made the key 3" long. This is obviously not the best way to do it, because the excess key stock length (to offset the unused shaft key slot) is at a further distance from the center of rotation of the shaft. However, this was a quick logical shot in the dark to get us close, and made things much better, but not perfect. Since then, I have had some time and I've been trying to find an exact formula. I have yet to come up with such a formula, so for now I've added a correction factor to offset the "overshot" in our first formula. I don't know if we're doing it right, but here's how I do it now: (shaft slot length * shaft slot depth * key stock width) + (bushing slot length * bushing slot height * key stock width) / (key stock width * key stock height). The answer ends up being the length (inches) of the key stock that would equal the volume of the shaft key slot + the volume of the bushing key slot. I then take 95% of that number and use that as correct key length. (The 95% was an average (91%-98%) of all the different key combinations and shaft sizes and speeds that we see).

So far this seems to work out real good, but I know it's still not perfect. What does everybody think, am I splitting hairs to get it any more precise then that? Is there some kind of formula already out there that I don't know about?

My buddy Ian McKinnon gave us pretty much the same equation you're using: [(hub length+keyway length)/2]*0.95. The 95% being the fudge factor due to how the end of the keyway is milled. And like you said, it's really close for most everything. The problem I had was with bastard keys, stepped keys and that we were assuming a rectangular volume. What about that little curved piece at the top of the shaft (called a circular segment)? How much did this affect the key length?

So I wrote a little program in Access to put in all the parameters--shaft size, key width, key height, hub length, keyway length and keyseat depth. With all that I could calculate a little closer the exact amount of material removed from the shaft and hub and what had to be put back. I still had to fudge the end section of the keyway--never pursued figuring out the differences between using a vertical end mill or horizontal end mill to cut the keyway. You could then choose a full key or a stepped key (to put more metal in the keyway). I started working on a way to make a drawing that we could give to the machine shop but didn't quite get it finished before I parted ways. Take a look--I'd love any feedback.

So, no, I don't think you're splitting hairs.

Demo_Keyway.mdb (2,708 Kb, 90 downloads)

For square keys, the key should fill the slot in the hub (or bushing), plus fill half of the "exposed keyway". Since most keyways have a radius at one end, I measure to the middle of the radius when determining the "exposed" keyway dimension.

Anyone use ISO 8821:1989,
Mechanical vibration - Balancing - Shaft and fitment key conversion?

This is currently up for the 5-year systematic review.

Lawrence, I like your access program.

Here's the Excel program I wrote.

key_length_calculator.xls (48 Kb, 87 downloads) Key Length Calculator

Terry had a maintenance tip that used a formula that equated to what Rusty uses. I passed it out to all our mechanics to use when they make changes to sheaves.
Simplicity is what counts. If you make it too involved it will become a curiosity and not a procedure. Being that close to the center of rotation, it doesn't have the impact it would farther out.

Under informative Annex C, ISO mentions for practical considerations of the final key:

Lk – length of keyway
Lf - length of fitment
La – average length of key

La = (Lk+Lf)/2

This is equivalent to Rusty’s comments.

I always just balance shafts with a half key the full length of the slot, then use step cut keys. Balancing at fan, motor, and pump vendors seems to be done with a full length half key (simulates solid shaft) so we also use step cut keys on everything, even if we don't balance it ourselves. Seems to work very well.

Jon, I developed my "simplified" explanation to use with mechanics. When I explain it that way, they go "oh yea, I get it"... it makes sense to them. After I get their "thinking calibrated" then I give them Bill's equation. While the equation is not perfect, it's usually close enough. For high speed equipment, Ed's stepped key is the better solution.

What I usually see is either the key doesn't extend into the exposed keyway at all, or the key completely fills the keyway.... doesn't seem to be much middle ground with most folks.

Nice Rpogram Bill S.

I like it alot , very visual. I could not get Lawrences to work

Nice little spreadsheet, Bill S... but I was wondering why you multiply by 0.95 at the end?

We always measured to the back of the keyway and multiplied by the 0.95 to 'adjust' for the radius at the end.

Bill,
I usually saw the exposed key parallel to the shaft but slightly up, saw the key square to the shaft at the back of the coupling / sheave, then dress the sawn key with a file, down as far as practical to the shaft. It saves calculations and usually works providing that the shaft had been balanced with a half key.
Regards,
Joe Mc Cormack